Summer Work

Packet for MPH

Math Classes

Students going into

Pre-calculus AC

Sept. 2018

Name: _____________________

This packet is designed to help students stay

current with their math skills.

Each math class expects a certain level of

number sense, algebra sense and graph sense

in order to be successful in the course.

These problems need to be completed in the

space provided and handed in for a grade by

September 7th. Be sure to show all work.

Please email me at dmeehan@mphschool.org

with any questions.

************************************** ** You will need a TI-84 calculator for this class.**

********************************************

Linear Functions & Inequalities Name ____________________

1. Given: 6x – 4y = 12.

A. Find the coordinates of the x-intercept: ________ and y-intercept: ________ .

B. Use these to calculate the slope. m = _____

C. Write the equation of a line parallel to the given line and going through the point

(0, –3).

D. Graph both lines below.

2. Given: m = – ½ and A (– 2, 5) Name ____________________

A. Write the equation of the line in point-slope form: ______________________

B. Write the equation of the line perpendicular to the given line going through

the point (4, 5) in point-slope form. _________________________

3. Given: (y – 3) = ¾(x + 5)

A. Name a point on the line. P ( ___, ___ )

B. Find the slope. m = _________

C. Find f(–9). f(–9) = _______

4. Graph the inequalities. Name the points of intersection. Label the solution

area. Show your check to verify the shaded area is correct.

y > ⅔x – 2 and y ≤ – x – 3 and x < 3

System of Equations Name ____________________

Solve for the variables using the elimination method. Check.

1. 5k + 9h = 13 2. a + b + c = 6

6k + 4h = 2 2a + b – 2c = – 10

a + 4b + c = 2

Solve for the variables using the substitution method. Check.

3. y = 5x – 12

5x – 2y = 124

Algebra Review: Simplify completely. Name ____________________

1.

x

x

431

52

3

2. ba

ba

11

3. yx

yxyxyx4

83454

4

41628

Name ____________________

4. )72303)(3612(

)242)(1083(22

232

yyyyy

yyyy (Leave your answer in factored form.)

5. 1

123

4

mmm

m (Leave your answer in factored form.)

6. 2

18

1215

32 bcabccab

Name ____________________

7. mn

nm

nm

nm

824

44

99

186

(Leave your answer in factored form.)

8. 3148

376

3108

31162

2

2

2

aa

aa

aa

aa (Leave your answer in factored form.)

9. 22

2

22

2

22

22

189

2

1211

6

32

2

baba

bab

baba

aba

baba

abba

(Leave your answer in factored form.)

10. yx 4

3

6

5 Name ____________________

11. 4

1

2 2

xx

x

12. 1011

4

100

722

ddd

13.12

3

21

2

14

72

xxx

Algebra Review: Solve and check. Name ____________________

14. w2 + 8w + 7 = 0 15. 3b3 + 13b = 7b2

16. 2p3 + p2 – 8p – 4 = 0 17. 22

15

h

18. cccc

2

1

1

23 19. 2

4

21

62

5

c

c

c

20. 4

12

1273 2

2

a

a

aa

a

a

a

Functions Name _________________________

Fill in the blanks with a rule to represent 3 different situations. Write two that represent a

function and one that do not. Explain why each is or is not a function.

Ex. 1: The number of loads of laundry I do is a function of the number of people at home during

the week.

Ex. 2: The fraction of the pool that is filled with water is a function of the amount of time the

hose has been filling it.

Ex. 3: The age of each person in the class is dependent on the numbers 15, 16 and 17. (More

than one person could be each age, or someone could be a different age.)

1. ______________________________ is _________________________________________

Function? Yes or No? Why?

2. ______________________________is _________________________________________

Function? Yes or No? Why?

3. ______________________________ is _________________________________________

Function? Yes or No? Why?

Odd and Even Functions Name ____________________

Prove algebraically that the function is odd, even or neither. Choosing a numerical value for x

does NOT prove odd/even. It must be shown true for ALL values of x. Follow the example.

Definition: f(x) is odd, if f (–x) = –f (x). f(x) is even, if f (–x) = f (x).

Otherwise, the function is neither odd nor even.

Example: f(x) = 4x3 – 5x

Find f(–x): f(–x) = 4(–x)3 – 5(–x) = –4x3 + 5x. Thus, f(–x) ≠ f(x).

Find –f(x): –f(x) = – (4x3 – 5x) = –4x3 + 5x. Thus, –f(x) = f(–x) and the function is ODD.

1. f(x) = 6x

2. f(x) = x2 – 4

3. f(x) = (x – 5)2

4. f(x) = x4

1

5. f(x) = 3 22 1

xx

6. f(x) = x3 – 3x2 + 3x – 1

Quadratic Inequalities and Sign Patterning Name ____________________

Use the number lines to indicate the sign of each factor. From this, determine the intervals

of x values which make the inequality true.

EXAMPLE 1: 4x3 ≥ 4x2 + 24x EXAMPLE 2: 0)2(

)3(

x

xx

4x3 – 4x2 – 24x ≥ 0 Use the same number lines because

4x (x2 – x – 6 ) ≥ 0 multiplication and division with negative

4x (x – 3)(x + 2) ≥ 0 numbers have the same rules.

factor value: negative negative 0 positive positive factor

4x

x values: -2 0 3

negative negative negative 0 positive (x – 3)

-2 0 3

negative 0 positive positive positive (x + 2)

-2 0 3

expression: negative *0 positive 0 negative 0 positive x(x – 3)(x + 2)

-2 0 3

Therefore, the solution set for Example 1 is {x| –2 ≤ x ≤ 0 or x ≥ 3}.

Therefore, the solution set for Example 2 is {x| x < –2 or 0 < x < 3}. (Example 2 is undefined

at x = –2.*)

Name ____________________

Find the solution set using the sign patterning method. Graph the solution on a number

line.

1. w2 – 7w < 0

2. 30 + c – c2 ≤ 0

3. 18x3 ≤ 2x

4. (2 – p)(4 – p)(7 – p) > 0

5. 06

k

k

6. 05

3

x

7. 02

2832

g

gg

Logarithms-Solve & check. Show work. Name ____________________

1. 3)1(log 4 x

2. 5)(log 2

3 x

3. )64(log)2(log 55 xx

4. )3(log)4(log 5

2

5 xx

5. 1)2log()1log( xx

Reference Angles & Trig Functions Name ____________________

1) Using the unit circle, give the exact value of each trigonometric expression. Pay

attention to the sign of the answer (no calculator).

2) On the unit circle mark the letter of each problem in the correct angle position.

Letter a is done for you.

a) sin(π) __0__

b) cos(5π/4) _____

c) tan(11π/6) _____

d) cot(22π/3) _____

e) sec(13π/2) _____

f) csc(28π) _____

g) sin(41π/6) _____

h) tan(–7π/3) _____

i) csc(–19π/4) _____

j) cos(14π) _____

k) sec(13π/4) _____

l) tan(19π/3) _____

m) cot(–17π) _____

n) sin(47π/3) _____

o) cos(–11π/6) _____

p) sin(–27π/4) _____

a

Graphing Functions Name ____________________

Graph the following functions on the graph below. Be sure to label your axes and

identify the scale on each axis. Do each pair in the question on the same set of axes.

1. y = x2 y = ½ x2

2. y = √𝑥 y = −2√𝑥

3. y = 2𝑥 y = 2𝑥−3 Name ____________________

4. y = log3(x) y = log3(x) + 2

Name ____________________

5. y = sin(x) y = cos(x)

Graph from –2π to 2π. Use 6 BLOCKS = π on the x-axis and 2 BLOCKS = 1 on the y-axis. (If

you use your calculator, be sure to put it in radian mode and use ZOOM TRIG for the window.)